Seasonal Adjustment And X13

Seasonal adjustment and X-13

A seasonally adjusted number is an estimate, and the agency re-estimates it every month. The unadjusted data for a month settles in about two months. The published adjusted value for that same month keeps moving for years — not because anyone collected anything, but because the seasonal factors were recomputed.

../real-time-macro-backtesting/SKILL.md owns revisions to the value. This skill owns the revision that arrives with no new information at all, which is invisible to every diagnostic built for the first kind.

Everything marked ✅ Measured is printed by scripts/seasonal_adjustment.py (numpy + pandas, seed 20260909, about 3 s, no network; statsmodels probed inside a function). Everything marked ✅ source-verified was read at the URL given on 2026-09-09.

1. ✅ What the agency says it does

✅ source-verified at bls.gov/web/empsit/cesseasadjtn.htm, verbatim:

"The CES program employs a concurrent seasonal adjustment methodology to seasonally adjust its national estimates of employment, hours, and earnings."

"Under concurrent methodology, new seasonal factors are calculated each month using all relevant data up to and including the current month period."

"Once a year, BLS seasonally adjusts CES series again, replacing the most recent 5 years of historical estimates with newly seasonally adjusted estimates."

— using "the U.S. Census Bureau's X-13ARIMA-SEATS application."

✅ source-verified at bls.gov/web/empsit/cesvininfo.htm: "CES estimates are subject to revisions for up to 2 months from their original publication due to ongoing receipt of sample data."

🔑 Put those two together and the trap states itself. Past the two-month window the unadjusted number is settled. Anything the published seasonally adjusted value does after that is arithmetic, and it happens twelve times a year, and again over five years of history at each annual re-adjustment.

⚠️ The annual benchmark compounds it from the other direction: ✅ source-verified at bls.gov/web/empsit/cesbmart.htm, "Twenty-one months of not seasonally adjusted CES estimates for all data types are revised based on this new March level, prior to seasonal adjustment", and the March-2025 benchmark moved the SA level by −898,000 against −862,000 NSA. The extra 36,000 is the seasonal adjustment reacting to the new NSA history. ../real-time-macro-backtesting/SKILL.md §1 has that table month by month.

2. The mechanism, in one paragraph

X-11's core is ratio-to-moving-average: estimate the trend with a centred 2x12 moving average, form SI ratios (data / trend), smooth each calendar month's SI ratios across years, normalise. 🔑 A centred filter does not exist for the last six months. The newest factors are one-sided extrapolations; when six more months arrive they become centred, and they change. That is not a flaw in the implementation — it is why concurrent adjustment revises at all, and no filter choice removes it.

scripts/seasonal_adjustment.py implements exactly that core in ~40 lines of numpy, so the effect is visible rather than delegated to a binary that is not installed. It is not a substitute for X-13: no RegARIMA pre-adjustment, no outlier detection, no trading-day or holiday regressors, no SEATS.

3. ✅ Measured — how far a settled month's published value moves

Synthetic monthly series, 300 months, seasonal amplitude 8.2 % of level at its widest and slowly evolving, irregular noise 0.35 %. Month-on-month movement in the published SA value for a month age months back, in percent of level:

⚠️ Ages 1–3 move by an identical amount here because this simplified filter gives every month inside the un-centred tail one shared end-normaliser; X-13's asymmetric end filters differ in that detail. The rows that carry the point are 6 and beyond.

🚨 The largest single rewrite lands at age 6 — the month the centred trend filter finally reaches it: 0.23 % on average and 1.02 % at worst, in one month, on a number nobody collected any new data about. ✅ Measured over its life, a settled month's published SA value ends 0.204 % from where it first settled (max 0.576 %) and travels 0.668 % getting there.

On US total nonfarm's ~158 million level, 0.01 % is 15,800 jobs — so the 12-month-old row (0.0157 %) is about 25,000 jobs a month arriving from nowhere, on a series whose mean absolute first-to-third sample revision is 51,000.

4. 🚨 Measured — the phantom signal

For each of 203 months, the over-the-month change as it was published at the time against as it appears in the series you download today:

🚨 26.1 % of the variation in the change you read today was not in the change that existed at the time, and the sign differs in 20.2 % of months. None of that is new data — every month here is at least three months old. A momentum, acceleration or surprise feature computed on today's SA history is partly reading a factor update that arrived after the decision it is supposed to inform.

🔑 And the re-adjustment is not wrong — that is what makes it dangerous. ✅ Measured against the true adjusted series: the settled concurrent estimate has RMSE 0.187 %, the real-time one 0.305 %. Re-adjustment genuinely improves the history. It just makes it a different series from the one anyone traded.

5. ✅ Measured — three regimes, and what each one buys

🔑 That is the whole trade in one table: accuracy of the history against stability of the history. Frozen factors are the least accurate on a series whose seasonality drifts, and they are the only ones that never rewrite a published value. A backtest needs the second column.

The practical form: keep the NSA vintage series, estimate your own factors on the data available at each decision date, and never let a later factor estimate touch an earlier published value. If you must use the agency's SA series, carry its vintages (../real-time-macro-backtesting/SKILL.md §2 lists the sources) and say which you used.

6. ✅ X-13ARIMA-SEATS in Python

✅ source-verified at census.gov/data/software/x13as.html (page updated 2025-07-10): "X-13ARIMA-SEATS is seasonal adjustment software produced, distributed, and maintained by the Census Bureau", offering "ARIMA model-based seasonal adjustment using a version of the SEATS software" as well as "nonparametric adjustments from the X-11 procedure", distributed "for Windows® PC and Linux/Unix platforms".

🚨 pip install statsmodels does not install the adjustment engine. ✅ source-verified in statsmodels/tsa/x13.py (statsmodels 0.15.0, read in the installed package):

BINARY_NAMES = ("x13as", "x12a", "x13as_ascii", "x13as_html")
BINARY_NAMES += tuple(f"{name}.exe" for name in BINARY_NAMES)   # windows

_find_x12 searches X13PATH, then X12PATH, then an explicit x12path=. With none of them, ✅ Measured by running it on this machine:

statsmodels.tools.sm_exceptions.X13NotFoundError:
x12a and x13as not found on path. Give the path, put them on PATH, or set the
X12PATH or X13PATH environmental variable.

The wrapper writes a spec file, shells out to the Census binary and parses its output; with no binary it raises before doing any work. Download the binary from Census and set X13PATH. 🔑 That also means X-13 is not reproducible from a requirements.txt — pin the binary version in your environment notes the way you pin a package.

⚠️ What you are likely to reach for instead, and what it is not. statsmodels.tsa.seasonal.seasonal_decompose is a plain ratio-to-moving-average with a single fixed seasonal profile — no evolving seasonality, no outlier handling, no calendar effects. STL (Cleveland et al.) does allow the seasonal to evolve and is a reasonable in-house choice, but neither reproduces an agency's published SA series, and using one to "check" an official number compares two different estimators. Both are in ../../../fin-models/skills/time-series-forecasting-models/SKILL.md's territory as decomposition tools; the point here is that they are your adjustment, so they are stable and point-in-time — which for a backtest is the property that matters.

7. Traps

• 🚨 Treating the SA series as data rather than as an estimate. §3–4.
• 🚨 Computing a change or a momentum feature on today's SA history. §4: a quarter of its variation and a fifth of its signs were not there at the time.
• 🚨 Diagnosing SA revisions with a vintage tool built for value revisions. A first-to-third revision table will show nothing: the NSA input never changed.
• 🚨 Mixing SA and NSA in one model. A ratio, a spread or a regression between an SA and an NSA series inherits the full seasonal on one side. Check both series' units and adjustment status before every join; FRED series IDs often differ only in a suffix.
• 🚨 Residual seasonality after aggregation. Summing or differencing independently adjusted components does not give an adjusted aggregate, and quarterly GDP has a documented history of residual seasonality. If your "adjusted" series still shows a calendar-month pattern in its residuals, it is not adjusted.
• 🚨 Assuming an agency uses concurrent adjustment. CES does — ✅ verified. Other programmes and other countries publish projected factors, sometimes a year ahead, and some publish the factors themselves. ⚠️ Check the specific programme's technical note; do not generalise from CES.
• 🚨 Comparing your own STL/seasonal_decompose output with the official SA series and calling the difference an error. They are different estimators. The comparison that means something is your own adjustment against itself at two vintages.
• 🚨 The adjustment method is a trial. Concurrent vs projected vs frozen, X-11 vs SEATS, the seasonal filter length, whether to log. Log them in ../../../fin-core/skills/backtest-validation/scripts/trial_ledger.py.

❓ Not verified

Which non-CES US programmes use concurrent versus projected factors · whether BEA's GDP seasonal adjustment carries published vintages · the exact asymmetric end filters X-13 uses (this script's simplified end handling is stated as such in §3) · the current X-13ARIMA-SEATS version number (the Census page showed an update date of 2025-07-10 but no version in the text that was retrieved).

8. Scripts and where this sits

scripts/seasonal_adjustment.py — the X-11 ratio-to-moving-average core with time-varying factors, the three publication regimes (concurrent / projected / frozen) as publication-date x reference-month matrices, the rewrite profile and settled-drift measures, the phantom-signal decomposition, the accuracy comparison, and the X-13 availability probe. numpy + pandas, seed 20260909, about 3 s; statsmodels imported inside a function and the demo degrades gracefully without it or without the Census binary.

• Revisions to the unadjusted value, and the vintage A/B — ../real-time-macro-backtesting/SKILL.md.
• Why the unemployment rate barely revises and payrolls do — ../macro-regime-and-recession-indicators/SKILL.md §4.
• When each print lands — ../macro-release-calendar-and-embargo/SKILL.md.
• Feeding an adjusted or unadjusted series to a mixed-frequency factor model — ../gdp-nowcasting-dynamic-factor/SKILL.md.
• Decomposition and forecasting tools in general — ../../../fin-models/skills/time-series-forecasting-models/SKILL.md.
• Where the SA and NSA series come from — ../../../fin-core/skills/fundamental-and-macro-data/SKILL.md.